Be aware.. I think it took me 10 trades to get to the team I wanted, and it hurts chemistry, fans, and all of that like hell, so if you are key gaming, don't do it, it's better to wait until you are a free agent, if you're playing every game, you can do it. If a team isn't interested in you, they probably won't trade for you, so if they are red, don't bother.
And no, they don't have to be the three first.